Solve for $x$ : $6x^2 - 30x - 144 = 0$
Explanation: Dividing both sides by $6$ gives: $ x^2 {-5}x {-24} = 0 $ The coefficient on the $x$ term is $-5$ and the constant term is $-24$ , so we need to find two numbers that add up to $-5$ and multiply to $-24$ The two numbers $3$ and $-8$ satisfy both conditions: $ {3} + {-8} = {-5} $ $ {3} \times {-8} = {-24} $ $(x + {3}) (x {-8}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 3) (x -8) = 0$ $x + 3 = 0$ or $x - 8 = 0$ Thus, $x = -3$ and $x = 8$ are the solutions.